Calculation method of complex connected structure support displacement under earthquake action

Abstract

The invention discloses a method for calculating the displacement of a complex connected structure support under the action of an earthquake, and the method comprises the following steps: building a structural finite element calculation model which is used for carrying out the dynamic characteristic analysis of the support and the response spectrum analysis under the action of the earthquake; then seismic waves are selected based on the natural vibration periods of the connecting body and the tower; performing dynamic time-history analysis on the support according to the selected seismic waves to obtain the maximum displacement of the support under the action of each group of seismic waves; determining the weighted displacement of the support under the natural seismic waves according to the error between the frequency spectrum of each group of natural seismic waves on the natural vibration periodic point of the connector and the standard spectrum; calculating based on the weighted displacement of the support and the displacement of the support under the action of artificial seismic waves to obtain the final displacement of the support; and finally, selecting the support with the corresponding specification according to the final displacement of the support. The method can consider the frequency spectrum difference of different seismic waves on the vibration period point of the connector, and improves the reasonability of the calculation result of the support displacement.

Description

Technical Field

[0001] The present invention relates to the technical field of earthquake engineering, and particularly to a method for calculating the displacement of a support of a complex connected structure under earthquake action. Background Art

[0002] At present, the connection methods between building towers and connectors are divided into weak connections and strong connections. Among them, a weak connection means that the connector and the tower are connected by support forms such as sliding supports, rubber supports, friction pendulum supports, etc.; in order to determine the joint width setting between the connector and the tower and the safety of the structure, designers need to use time history analysis to supplement the calculation of the displacement of the support under earthquake action. On this basis, the current engineering calculation method for the support displacement is to first select waves according to the amplitude, frequency spectrum characteristics and duration of the seismic wave in accordance with the requirements of the "Code for Seismic Design of Buildings"; then use the structural finite element calculation model to perform dynamic time history analysis on the support according to the selected seismic wave to obtain the maximum displacement value of the support under different seismic waves; finally, calculate the final displacement result by taking the envelope value of 3 waves or the average value of 7 waves for each maximum displacement value.

[0003] However, the defect of the above calculation method is that, compared with the tower, the mass participation coefficient of the connector is relatively small, and the influence on the displacement of the support is also relatively small. As a result, the frequency spectrum characteristics considered in wave selection at present actually refer to the frequency spectrum characteristics of the seismic wave at the natural vibration period point of the tower, and the frequency spectrum characteristics of the seismic wave at the natural vibration period point of the connector will not be considered. However, for connectors such as link corridors, due to the relatively large discreteness of natural seismic waves, the influence of the vibration period of the connector itself on the displacement of the support is also very sensitive; that is, when the frequency spectrum of the seismic wave is close to the natural vibration period point of the tower and deviates greatly at the natural vibration period point of the connector, there will still be a large difference in the maximum displacement data of the support. This makes the current conventional method of selecting seismic waves and performing time history analysis based on the three elements of wave selection reduce the rationality of the calculation result of the support displacement.

[0004] Secondly, restricted by the three elements of wave selection, there will inevitably be a large deviation in the frequency spectrum characteristics of each seismic wave selected by designers at the natural vibration period point of the connector, and this results in that whether using the envelope value of 3 waves or the average value of 7 waves to calculate the support displacement will affect the calculation accuracy of the support displacement, that is, the displacement calculation result based on the seismic wave with a smaller difference from the natural vibration period point of the connector will be affected by the displacement calculation result with a larger difference, thereby reducing the accuracy of the final calculation result.

[0005] Therefore, the existing method for calculating the displacement of the support has the problem of poor rationality. Summary of the Invention

[0006] The object of the present invention is to provide a calculation method for the displacement of the supports of a complex connected structure under seismic action, which can take into account the differences in the spectra of different seismic waves at the vibration period points of the connection body and improve the rationality of the calculation results of the support displacements.

[0007] The technical solution of the present invention: A calculation method for the displacement of the supports of a complex connected structure under seismic action includes the following steps:

[0008] ① Establish a structural finite element calculation model, which is used for the dynamic characteristic analysis of the supports and the response spectrum analysis under seismic action;

[0009] ② Select seismic waves based on the natural vibration periods of the connection body and the towers, and the seismic waves include natural seismic waves and artificial seismic waves;

[0010] ③ Conduct a dynamic time-history analysis on the supports according to the selected seismic waves to obtain the maximum displacement of the supports under each group of seismic waves;

[0011] ④ Compare the spectral characteristics of the natural seismic waves with the code response spectrum based on the natural vibration period points of the towers and the connection body, and determine the weighted displacement of the supports under the natural seismic waves according to the error between the spectrum of each group of natural seismic waves and the code spectrum at the natural vibration period points of the connection body;

[0012] ⑤ Calculate based on the weighted displacement of the supports and the displacement of the supports under the artificial seismic waves to obtain the final displacement of the supports;

[0013] ⑥ Select the supports of the corresponding specifications according to the final displacement of the supports.

[0014] In the aforementioned calculation method for the displacement of the supports of a complex connected structure under seismic action, the modal mass participation coefficient of the structural finite element calculation model in the response spectrum analysis in step ① is greater than 90%.

[0015] In the aforementioned calculation method for the displacement of the supports of a complex connected structure under seismic action, the specific selection range of the seismic waves in step ② is as follows: The average seismic influence coefficient curve of the seismic waves differs from the code spectrum curve by no more than 20% at the natural vibration period points of the connection body and the towers, the average base shear force of the calculation results is not less than 80% of the code response spectrum method, the ratio of the calculation results of each seismic wave to the code response spectrum method is between 65% and 135%, and the effective duration is not less than 15 s.

[0016] In the aforementioned calculation method for the displacement of the supports of a complex connected structure under seismic action, when the seismic waves are subjected to dynamic time-history analysis in step ③, the loading ratios of the seismic waves in the X, Y, and Z directions are 1:0.85:0.65.

[0017] In the aforementioned method for calculating the displacement of the support of a complex connected structure under earthquake action, in step ④, the weighted displacement of the support under natural earthquake waves is calculated through the formula

[0018]

[0019] where n is the number of selected earthquake waves; e i and e j are the errors between the spectrum of the earthquake wave and the code spectrum at the corresponding vibration mode period points of the connected body in the direction of the support displacement; d i is the support displacement under the action of the i-th group of earthquake waves.

[0020] In the aforementioned method for calculating the displacement of the support of a complex connected structure under earthquake action, in step ⑤, when calculating the final displacement of the support, if the number of earthquake waves is less than seven groups, the final displacement of the support is taken as the envelope value of the weighted displacement of the support and the displacement of the support under artificial earthquake waves during calculation; if the number of earthquake waves is more than seven groups, the final displacement of the support is taken as the average value of the weighted displacement of the support and the displacement of the support under artificial earthquake waves during calculation.

[0021] In the aforementioned method for calculating the displacement of the support of a complex connected structure under earthquake action, in step ⑥, when selecting the support, it should be ensured that the limit of the selected support is not less than 1.2 times the final displacement of the support.

[0022] Compared with the prior art, the present invention has the following characteristics:

[0023] (1) By restricting the spectrum of the natural vibration period of the connected body when selecting earthquake waves, the present invention can effectively eliminate earthquake waves with a large difference from the natural vibration period of the connected body, thereby preventing the influence of this part of earthquake waves on the final calculation result in subsequent calculations and improving the rationality of the calculated result of the support displacement;

[0024] (2) By calculating the weighted displacement data of the support under natural earthquake waves, natural earthquake waves with a smaller difference from the natural vibration period of the connected body will have a greater weight in subsequent displacement calculations, while natural earthquake waves with a larger difference from the natural vibration period of the connected body will have a greater weight in subsequent displacement calculations. Furthermore, the calculated support displacement finally obtained is closer to the calculation data of natural earthquake waves with a smaller difference from the natural vibration period of the connected body, thereby further improving the rationality of the calculated result of the support displacement;

[0025] Therefore, the present invention can consider the differences in the spectra of different earthquake waves at the vibration period points of the connected body and improve the rationality of the calculated result of the support displacement. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is the calculation flow chart of the present invention;

[0027] Figure 2 It is the spectral characteristics of the selected natural earthquake waves in Experimental Example 1 and the error from the code spectrum;

[0028] Figure 3 It is the spectral characteristics of the selected natural earthquake waves in Experimental Example 2 and the error from the code spectrum. Specific implementation manners

[0029] The present invention will be further described below in conjunction with embodiments, but it shall not be used as a basis for limiting the present invention.

[0030] Embodiment. A calculation method for the displacement of the bearing of a complex connected structure under earthquake action, the steps are as Figure 1 shown, including the following steps:

[0031] ① Establish a structural finite element calculation model, which is used for dynamic characteristic analysis of the bearing and response spectrum analysis under earthquake action;

[0032] ② Extract the natural vibration periods of the tower and the connection body, and select earthquake waves based on the natural vibration periods of the connection body and the tower according to the requirements of the "Code for Seismic Design of Buildings", and the earthquake waves include natural earthquake waves and artificial earthquake waves;

[0033] ③ Conduct dynamic time history analysis on the bearing according to the selected earthquake waves to obtain the maximum displacement of the bearing under each group of earthquake waves;

[0034] ④ Compare the spectral characteristics of the natural earthquake waves with the code response spectrum based on the natural vibration period points of the tower and the connection body, and determine the weighted displacement of the bearing under the natural earthquake waves according to the error between the spectrum of each group of natural earthquake waves and the code spectrum at the natural vibration period point of the connection body;

[0035] ⑤ Calculate based on the weighted displacement of the bearing and the displacement of the bearing under the artificial earthquake waves to obtain the final displacement of the bearing;

[0036] ⑥ Select bearings of corresponding specifications according to the final displacement of the bearing.

[0037] In step ①, the participation coefficient of the modal mass of the structural finite element calculation model in the response spectrum analysis is greater than 90%.

[0038] In step ②, the specific selection range of the earthquake waves is as follows: the average earthquake influence coefficient curve of the earthquake waves differs from the code spectrum curve by no more than 20% at the natural vibration period points of the connection body and the tower, the average base shear force of the calculation results is not less than 80% of the code response spectrum method, the ratio of the calculation results of each earthquake wave to the code response spectrum method is between 65% and 135%, and the effective duration is not less than 15 s.

[0039] In step ③, when performing dynamic time history analysis on seismic waves, the loading ratios of seismic waves in the X, Y, and Z directions are 1:0.85:0.65.

[0040] In step ④, the weighted displacement D of the bearing under natural seismic waves is calculated by the formula

[0041]

[0042] where n is the number of selected seismic waves; e i 、e j is the error between the spectrum of the seismic wave and the code spectrum at the corresponding modal period point of the connecting body in the direction of the bearing displacement; d i is the bearing displacement under the action of the i-th group of seismic waves.

[0043] In step ⑤, when calculating the final displacement of the bearing, when the number of seismic waves is less than seven groups, the final displacement of the bearing is taken as the envelope value of the weighted displacement of the bearing and the displacement of the bearing under artificial seismic waves; when the number of seismic waves is more than seven groups, the final displacement of the bearing is taken as the average value of the weighted displacement of the bearing and the displacement of the bearing under artificial seismic waves.

[0044] In step ⑥, when selecting the bearing, it should be ensured that the limit of the selected bearing is not less than 1.2 times the final displacement of the bearing.

[0045] The working principle of the present invention: By limiting the difference between the spectrum characteristics of the seismic wave and the natural vibration period of the connecting body when selecting the seismic wave, the influence of the natural vibration of the connecting body on the bearing displacement can be taken into account when performing dynamic time history analysis on the seismic wave, so that the maximum displacement data of the simulated bearing is closer to being reliable. By weighted calculation of the maximum displacement of the bearing under natural seismic waves, the calculation weight of natural seismic waves with smaller differences between spectrum characteristics and the natural vibration period of the connecting body can be increased, and then the maximum displacement data of the bearing finally obtained is closer to the maximum displacement data of the bearing under the action of this natural seismic wave, thereby further improving the rationality of the calculation results.

[0046] Experimental example 1: In this experimental example, a certain high-rise complex weak connected structure is taken as the analysis object. The main buildings of the connected structure are the left and right twin towers of 2 high-rise office buildings. The left and right twin towers are connected to each other through a corridor. The left tower has 21 floors above ground and a building height of 99.9 m, and the right tower has 27 floors above ground and a building height of 127 m. Both main buildings of the twin towers adopt a steel pipe concrete column + concrete core tube structure. The corridor span is 40 m and it adopts a steel truss structure. The corridor and the tower are weakly connected by lead rubber bearings, with a total of 4 bearings on the left and right, numbered A - D.

[0047] Then, the calculation method of Example 1 is adopted to calculate the displacement of the lead rubber bearing under earthquake action; in step ①, the YJK software is used to establish a structural finite element calculation model, the wall panels are adopted with shell elements, the beam-columns are adopted with bar elements, and the lead rubber bearings are adopted with connection elements;

[0048] In step ②, the natural vibration periods of the left and right towers and the connecting corridor are shown in Table 1:

[0049] Table 1 Main Periods of the Structure (Unit: s)

[0050] Serial number Left tower Right tower Corridor 1 2.576 3.625 1.938 2 2.018 2.956 1.880 3 1.784 2.409 1.849

[0051] Considering comprehensively the first three natural vibration period points of the left and right towers and the natural vibration period points of the connecting corridor, 5 groups of natural earthquake waves and 2 groups of artificial earthquake waves, a total of 7 groups of earthquake waves are selected. The spectral information of the selected natural earthquake waves is as Figure 2 shown, Figure 2 in which the mark T6 is the natural vibration period of the connecting corridor in the X direction, T7 is the natural vibration period of the connecting corridor in the Y direction, T8 is the torsional natural vibration period of the connecting corridor, and T1 - T5 and T9 are the natural vibration periods of the left and right towers.

[0052] In step ③, the maximum displacements of the lead rubber bearing under the action of each group of natural earthquake waves obtained by dynamic time history analysis are shown in Table 2, and the maximum displacements of the lead rubber bearing under the action of each group of artificial earthquake waves are shown in Table 3:

[0053] Table 2 Maximum Displacements of the Bearing under the Action of Natural Earthquake Waves (Unit: mm)

[0054]

[0055] Table 3 Maximum Displacements of the Bearing under the Action of Artificial Earthquake Waves (Unit: mm)

[0056]

[0057] In step ④, at the natural vibration period points of the connecting corridor (1.938 in the x direction and 1.880 in the y direction), the spectral characteristics of the selected natural earthquake waves are compared with the code response spectrum, and the weighted displacements of the lead rubber bearing are calculated according to the errors between the spectra of each group of natural earthquake waves and the code spectrum at the natural vibration period points of the connecting corridor. The calculation results are shown in Table 4:

[0058] Table 4 Weighted Displacements of the Bearing under the Action of Natural Earthquake Waves (Unit: mm)

[0059]

[0060] Taking bearing A as an example, the final displacement in the X direction is calculated by the formula

[0061]

[0062] Calculated; the spectral values of each natural earthquake wave at the natural vibration period points and the spectral values of the code spectrum are both calculated according to the existing calculation methods. Taking the error value of 0.37% as an example, the spectral value of the first natural earthquake wave at the natural vibration period point T6 is 0.132497, and the spectral value of the code spectrum at the natural vibration period point T6 is 0.132994. The error value ei is calculated by (0.132497 - 0.132994) * 100% / 0.132994;

[0063] In step ⑤, the average value is calculated according to the results of Table 4 and Table 3 to obtain the final displacement of the lead rubber bearing, as shown in Table 5 specifically:

[0064] Table 5 Final bearing displacement (unit: mm)

[0065] Bearing number X direction Y direction A 192 157 B 190 149 C 180 164 D 181 162

[0066] Experimental Example 2: In this experimental example, the high-rise complex weak connected structure of Comparative Document 1 is used as the analysis object, and the existing method for selecting earthquake waves without considering the natural vibration period of the corridor and the method for calculating the bearing displacement are used for calculation. The calculation method is specifically as follows:

[0067] ① Use the YJK software to establish a structural finite element calculation model, in which the wall panels adopt shell elements, the beam-columns adopt bar elements, and the lead rubber bearings adopt connection elements;

[0068] ② Extract the natural vibration periods of the left and right towers. The natural vibration periods of the left and right towers are shown in Table 1; then, according to the natural vibration periods, the amplitudes and durations of the earthquake waves, 5 groups of natural earthquake waves and 2 groups of artificial earthquake waves are selected. The spectral information of the selected natural earthquake waves is as Figure 3 shown, Figure 3 The marks T1 - T6 in it are all the natural vibration periods of the left and right towers;

[0069] ③ Conduct a dynamic time history analysis on the bearing according to the selected earthquake waves to obtain the maximum displacement of the bearing under each group of earthquake waves, as shown in Table 6 and Table 7 specifically;

[0070] Table 6 Maximum bearing displacement under natural earthquake waves (unit: mm)

[0071]

[0072]

[0073] Table 7 Maximum bearing displacement under artificial earthquake waves (unit: mm)

[0074]

[0075] ④According to the "Code for Seismic Design of Buildings", the average value of the maximum displacements of the bearing under 7 groups of seismic waves is taken to obtain the final displacement of the bearing, as shown in Table 8 specifically:

[0076] Table 8 Calculation of the final bearing displacement by the conventional method (unit: mm)

[0077] Bearing number X direction Y direction A 149 138 B 148 133 C 130 141 D 143 142

[0078] ⑤Select the bearing with the corresponding specification according to the final displacement of the bearing.

[0079] By comparing the calculation results of Experimental Example 1 and Experimental Example 2, it can be seen that the maximum displacement data of the bearing obtained in the dynamic time history analysis for the seismic waves selected considering the natural vibration period of the connecting body and those not considering the natural vibration period of the connecting body are different, which results in differences in the calculation results of the final displacement of the bearing, indicating that the existing seismic wave selection method is not reasonable and is likely to cause distortion of the final calculation results.

[0080] Experimental Example 3: In this experimental example, the high-rise complex weak connected body structure of Comparative Document 1 is taken as the analysis object, 7 groups of seismic waves identical to those in Experimental Example 1 are selected, and the final displacement of the bearing is calculated by taking the average value according to the "Code for Seismic Design of Buildings" to obtain the final displacement of the bearing, as shown in Table 9 specifically:

[0081] Table 9 Calculation of the final bearing displacement by the conventional method (unit: mm)

[0082] Bearing number X direction Y direction A 152 140 B 151 135 C 138 153 D 143 150

[0083] Taking bearing A as an example, the final displacement in the X direction is calculated through the formula

[0084] D x =(228 + 118 + 108 + 119 + 129 + 177 + 184) / 7 = 152mm

[0085] and obtained.

[0086] By comparing the calculation results of Experimental Example 1 and Experimental Example 3, it can be seen that even though the same seismic waves are selected for the dynamic time history analysis in the two experimental examples, there are still significant differences in the final displacement data of the bearing obtained finally, indicating that the method of weighted calculation of the maximum displacement data of the bearing under natural seismic waves for the connecting body in this application can increase the weight of the natural seismic waves with smaller differences between the spectral characteristics and the natural vibration period points of the connecting body in the calculation process, making the calculation result closer to the maximum displacement value of the bearing under this natural seismic wave and making the final calculation result more accurate and reasonable.

Claims

1. A calculation method for the displacement of the support of a complex connected structure under earthquake action, characterized in that, It includes the following steps: ① Establish a structural finite element calculation model, which is used for dynamic characteristic analysis of the bearing and response spectrum analysis under seismic action; ② Select seismic waves based on the natural vibration periods of the connection body and the tower, and the seismic waves include natural seismic waves and artificial seismic waves; ③ Conduct dynamic time history analysis on the bearing according to the selected seismic waves to obtain the maximum displacement of the bearing under each group of seismic waves; ④ Compare the spectral characteristics of the natural seismic waves with the code response spectrum based on the natural vibration period points of the tower and the connection body, and determine the weighted displacement of the bearing under the natural seismic waves according to the error between the spectrum of each group of natural seismic waves and the code spectrum at the natural vibration period point of the connection body; ⑤ Calculate based on the weighted displacement of the bearing and the displacement of the bearing under the artificial seismic waves to obtain the final displacement of the bearing; ⑥ Select a bearing with a corresponding specification according to the final displacement of the bearing.

2. The calculation method for the displacement of the bearing of a complex connected structure under seismic action according to claim 1, characterized in that: In step ①, the participation coefficient of the modal mass in the response spectrum analysis of the structural finite element calculation model is greater than 90%.

3. A calculation method for the displacement of the bearing of a complex connected structure under earthquake action according to claim 1, characterized in that, The specific selection range of the seismic waves in step ② is as follows: the average seismic influence coefficient curve of the seismic waves differs from the code spectrum curve by no more than 20% at the natural vibration period points of the connection body and the tower, the average bottom shear force of the calculation results is not less than 80% of the code response spectrum method, the ratio of the calculation results of each seismic wave to the code response spectrum method is between 65% and 135%, and the effective duration is not less than 15 s.

4. The calculation method for the displacement of the bearing of a complex connected structure under earthquake action according to claim 1, wherein: In step ③, when the seismic waves are used for dynamic time history analysis, the loading ratios of the seismic waves in the X, Y, and Z directions are 1:0.85:0.

65.

5. A calculation method for the displacement of the support of a complex connected structure under seismic action according to claim 1, characterized in that: In step ④, the weighted displacement of the bearing under the natural seismic waves is obtained through the formula Calculated, where n is the number of selected seismic waves; e i , e j is the error between the spectrum of the seismic wave and the code spectrum at the corresponding modal period point of the connection body in the direction of the support displacement; d i is the support displacement under the action of the i-th group of seismic waves.

6. The calculation method for the displacement of the support of a complex connected structure under seismic action according to claim 1, wherein: When calculating the final displacement of the bearing in step ⑤, when the number of seismic waves is less than seven groups, the final displacement of the bearing is taken as the envelope value of the weighted displacement of the bearing and the displacement of the bearing under the artificial seismic waves when calculating; when the number of seismic waves is more than seven groups, the final displacement of the bearing is taken as the average value of the weighted displacement of the bearing and the displacement of the bearing under the artificial seismic waves when calculating.

7. A calculation method for the displacement of the support of a complex connected structure under seismic action according to claim 1, characterized in that: When selecting the bearing in step ⑥, it should be ensured that the limit of the selected bearing is not less than 1.2 times the final displacement of the bearing.

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